New pressure for the prime minister to take steps to overturn the Labour government's hunting ban returned this Christmas with two government ministers breaking ranks to call for action on the issue ahead of the Boxing Day hunt.

Agriculture minister Jim Paice, the Tory MP for South East Cambridgeshire, who has ministerial responsibility for overseeing the ban on hunting with dogs, told the Sunday Times that the current system "isn't working" and was making a "mockery" of the law.

Instead of an outright ban on the practice, the Hunting Act allows the use of a pair of hounds to flush out a fox which is then shot. Exercising packs of hounds and following scented trails are also permitted and there has arisen ambiguity over when a hunt has seen hunters deliberately set their dogs on foxes and when a kill has been accidental.

Today the Countryside Alliance estimates that more than 250,000 people will take part in more than 300 of these now constrained Boxing Day hunts.

The coalition agreement states that there will be a free vote on whether or not to repeal the 2005 legislation staged some time before the next election in 2015 but no vote has yet been tabled and now two of David Cameron's ministers push the prime minister for action.

Jim Paice said: "The current law simply doesn't work. I am personally in favour of hunting with dogs and the coalition agreement clearly states that we will have a free vote on whether to repeal the act when there is time in the parliamentary calendar to do so."

He said there were "absurdities" in the hunting legislation. He said: "Frankly, it is a mess. It has been criticised by virtually all levels of authority — by the courts, by the police — as unenforceable. Efforts by the pressure groups to force the police to enforce it are just distracting the police from more important issues."

"To me the whole thing is making the law a bit of a mess and making a bit of a mockery of it," Paice said.

He received support from Richard Benyon, a fellow Defra minister and Tory MP for Newbury in Berkshire, who said: "I have been and remain a supporter of hunting and believe the Hunting Act has been bad for the countryside and bad for wildlife."

As recently as 2010 Cameron described himself as a "country boy" and said he believed the ban, introduced under Labour in 2005, was a "mistake". Some Tory MPs call for the ban to overturned and replaced with a stricter system of regulation.

However, a number of modernising Tory MPs - known as the Blue Fox group - have described the prospect of a vote on hunting as "dead and buried". This group is thought to number around 20 MPs. Many Lib Dems would join them in resisting the repeal of the legislation but the move to overturn the hunting ban could be joined by a number of Labour MPs making it unclear what way a Commons' vote would go.